Answer:
x2-14x+58=0
Two solutions were found :
x =(14-√-36)/2=7-3i= 7.0000-3.0000i
x =(14+√-36)/2=7+3i= 7.0000+3.0000i
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-14x+58
The first term is, x2 its coefficient is 1 .
The middle term is, -14x its coefficient is -14 .
The last term, "the constant", is +58
Step-1 : Multiply the coefficient of the first term by the constant 1 • 58 = 58
Step-2 : Find two factors of 58 whose sum equals the coefficient of the middle term, which is -14 .
-58 + -1 = -59
-29 + -2 = -31
-2 + -29 = -31
-1 + -58 = -59
1 + 58 = 59
2 + 29 = 31
29 + 2 = 31
58 + 1 = 59
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 14x + 58 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-14x+58
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 7.0000
Plugging into the parabola formula 7.0000 for x we can calculate the y -coordinate :
y = 1.0 * 7.00 * 7.00 - 14.0 * 7.00 + 58.0
or y = 9.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-14x+58
Axis of Symmetry (dashed) {x}={ 7.00}
Vertex at {x,y} = { 7.00, 9.00}
Function has no real roots
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-14x+58 = 0 by Completing The Square .
Subtract 58 from both side of the equation :
x2-14x = -58
Now the clever bit: Take the coefficient of x , which is 14 , divide by two, giving 7 , and finally square it giving 49
Add 49 to both sides of the equation :
On the right hand side we have :
-58 + 49 or, (-58/1)+(49/1)
The common denominator of the two fractions is 1 Adding (-58/1)+(49/1) gives -9/1
So adding to both sides we finally get :
x2-14x+49 = -9
Adding 49 has completed the left hand side into a perfect square :
x2-14x+49 =
(x-7) • (x-7) =
(x-7)2
Things which are equal to the same thing are also equal to one another. Since
x2-14x+49 = -9 and
x2-14x+49 = (x-7)2
then, according to the law of transitivity,
(x-7)2 = -9
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-7)2 is
(x-7)2/2 =
(x-7)1 =
x-7
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-7 = √ -9
Add 7 to both sides to obtain:
x = 7 + √ -9
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 - 14x + 58 = 0
has two solutions:
x = 7 + √ 9 • i
or
x = 7 - √ 9 • i
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-14x+58 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -14
C = 58
Accordingly, B2 - 4AC =
196 - 232 =
-36
Applying the quadratic formula :
14 ± √ -36
x = ——————
2
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -36 =
√ 36 • (-1) =
√ 36 • √ -1 =
± √ 36 • i
Can √ 36 be simplified ?
Yes! The prime factorization of 36 is
2•2•3•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 36 = √ 2•2•3•3 =2•3•√ 1 =
± 6 • √ 1 =
± 6
So now we are looking at:
x = ( 14 ± 6i ) / 2
Two imaginary solutions :
x =(14+√-36)/2=7+3i= 7.0000+3.0000i
or:
x =(14-√-36)/2=7-3i= 7.0000-3.0000i
Two solutions were found :
x =(14-√-36)/2=7-3i= 7.0000-3.0000i
x =(14+√-36)/2=7+3i= 7.0000+3.0000i
R
Step-by-step explanation:
The roots of the given quadratic equation are (7+i) and (7-i).
The given quadratic equation is:
[tex]x^{2} -14x=-50[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.
We can write the above equation as:
[tex]x^{2} -14x+50=0[/tex]
Using the Shreedharacharya formula to solve a quadratic equation
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(-14)+-\sqrt{(-14)^2-4*1*50} }{2*1}[/tex]
[tex]x=7+i\\x=7-i[/tex]
Where i=√-1
Hence, the roots of the given quadratic equation are (7+i) and (7-i).
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The formula y equals 15 left parenthesis 1.26 right parenthesis to the power of x gives the number of cellular phone users y (in millions) in some country for the years 1994 through 2006. In this formula, x = 0 corresponds to 1994, x = 1 corresponds to 1995, and so on. Use this model to predict the number of cellular phone users in the year 2006.
The predicted number of cellular phone users in the year 2006 is __________ million. (Round to the nearest whole number as needed.)
Final answer:
Using the formula y = 15(1.26)^x and setting x to 12 for the year 2006, we calculate that the predicted number of cellular phone users in that year is approximately 84 million.
Explanation:
The formula y = 15(1.26)^x is used to predict the number of cellular phone users in millions for a given year, with x representing the number of years since 1994. In this case, we want to find the predicted number of cellular phone users for the year 2006. Since 2006 is 12 years after 1994, we will set x = 12.
Plugging in this value, the equation becomes y = 15(1.26)^12. To find the answer, we must calculate 1.26 raised to the power of 12 and then multiply the result by 15.
Calculating this gives us y = 15(1.26)^12 ≈ 15 * 5.582 ≈ 83.73 million, which we round to 84 million cellular phone users.
Final answer:
The predicted number of cellular phone users in the year 2006 is 63 million.
Explanation:
To predict the number of cellular phone users in the year 2006 using the formula y = 15(1.26)^x, we need to determine the value of x that corresponds to the year 2006. We know that x = 0 corresponds to 1994, so the year 2006 would be 12 years later. Therefore, x = 12.
Substituting x = 12 into the formula, we have y = 15(1.26)^12.
Calculating this expression gives us y ≈ 63.273.
Rounding to the nearest whole number, the predicted number of cellular phone users in the year 2006 is 63 million.
HELP i need help with this!!!
Answer:
A=26.75
Step-by-step explanation:
A=1/2(2)(2)=2
A=1/2(5)(2)=5
A=1/2(2+2+5)(3.5)=15.75
A=2+5+15.75=26.75
Omg 1+1 totally doesn’t even 2
Lemme stop acting slow
I don’t know how to do the work I just don’t understand
Answer:
1. is -5/7
2. is 6/-9 OR 1/-3 (negative one third)
3. is 2
Step-by-step explanation:
How does the shape of a cross-section of a 3D figure parallel to the base relate to the volume of the 3D figure?
Answer:
The volume of a 3D figure can be determined by the sum of all the cross-sections of that 3D figure parallel to the base
Step-by-step explanation:
We need to understand what a cross-section of a 3D figure ?
A cross section is the shape we get when cutting straight through an object
and in geometry it is the shape made when a solid is cut through by a plane.
=> the cross section is parallel to the base of the figure.
So that the area of the cross-section is determined by its shape
Hence, The volume of a 3D figure can be determined by the sum of all the cross-sections of that 3D figure parallel to the base
The shape of a cross-section parallel to the base of a 3D figure determines its volume, as the volume is calculated by multiplying this area by the figure's height. For parallelepiped figures, the cross-sectional area is found using the magnitude of the cross product of base side vectors.
Understanding the relationship between the shape of a cross-section and the volume of a three-dimensional figure involves recognizing that for solids with parallel sides, such as a cylinder or parallelepiped, the cross-section parallel to the base will have the same shape as the base. When this cross-section is multiplied by the height of the figure, the result is the volume of that shape (V = Ah). In terms of vectors representing the base in three-dimensional space, for a parallelepiped, the cross-sectional area can be found by the magnitude of the cross product of vectors given by the sides forming the base.
Moreover, regardless of changes in length or width, as shown in Table 3, if a volume is kept constant but the shape is altered to be elongated or flattened, the shape of the cross-section parallel to the base still determines the volume through the base area times the height formula.
This is significant in various fields, including physics, engineering, and architecture, where understanding the volume and dimensions of structures and shapes is crucial.
Mrs. Williams estimates that on average her family recycles 12.6 pounds of plastic each month. In a year's time, how much landfill space will Mrs. William's family save if 1 pound of plastic saves 7.4 yards of landfill space?
a.
932.40 yards
b.
93.24 yards
c.
1,118.88 yards
d.
7.77 yards
Answer:B
Step-by-step explanation:
Mrs. Williams' family recycles 151.2 pounds of plastic in a year, and since 1 pound of plastic saves 7.4 yards of landfill space, their recycling efforts save approximately 1,118.88 yards of landfill space annually.
Explanation:To find out how much landfill space Mrs. Williams family can save in a year, we can start by calculating how much plastic they recycle in a year. This can be done by multiplying the monthly amount by the total number of months:
12.6 (pounds per month) x 12 (months per year) = 151.2 pounds of plastic
Next, we use the fact that every pound of plastic recycled saves 7.4 yards of landfill space. So, we multiply the total pounds of plastic by the amount of space saved per pound:
151.2 (pounds of plastic) x 7.4 (yards per pound) = 1,118.88 yards
Therefore, Mrs. Williams family can save approximately 1,118.88 yards of landfill space per year by their recycling efforts.
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Given: PRST square
PMKD is a square
PR = a, PD = a
Find the area of PMCT.
PLEASE HELPP
Answer:
7a²/16
Step-by-step explanation:
Area of the triangle PTS
½ × a × a
a²/2
Length of PS:
sqrt(a² + a²)
asqrt(2)
Length of MS:
¼asqrt(2)
Triangles MCS and TPS are similar
With sides in the ratio:
¼asqrt(2) : a
sqrt(2)/4 : 1
Area of triangle SMC:
A/(a²/2) = [(sqrt(2)/4)]²
2A/a² = 1/8
A = a²/16
Area of PTMC
= a²/2 - a²/16
= 7a²/16
Step-by-step explanation:
This is a much more interesting problem than what we usually see here.
Let's just start by assuming a=1 so we have two unit squares.
PMC and PTC are two congruent triangles, each right triangles with one leg of length 1 and a shared hypotenuse PC.
We'll put it on the grid at P(0,0), T(1,0).
Angle TPM is 45 degrees and PM=1 so
M(cos 45, sin 45) = M(1/√2, 1/√2)
MK has slope -1, thru M, so is
y = -x + √2
C's on that line at x=1, so C's x coordinate is 1, so its y coordinate is √2 - 1
C(1, √2 - 1)
OK, that's enough to compute the area.
P(0,0), T(1,0), C(1, √2 - 1), M(1/√2, 1/√2)
area(PMCT) = area(PTC) + area(PCM)= 2 area(PTC)
The area of a right triangle is half the product of its legs.
area(PMCT) = 2 (1/2) (1) ( √2 - 1)
area(PMCT) = √2 - 1
When we have sides a, the area scales by a²,
Answer: a²(√2 - 1)
Please help with this! :)
Answer:
4 and 3 <------- That's the set I believe!
For a biology assignment, Josephine records the height of a plant over
time. The plant was 12 cm tall when she started the assignment. She
notices that the plant grows 2 cm every week,
What point is on her graph ?
Answer:
3,18
Step-by-step explanation:
can anyone help me with this question??
Answer:
The answer is B
Step-by-step explanation:
You don't need elimination for this when you plug it in 10(-5) is equal to -50 add 5 to that to get -45
and -5(2)=-10 +5 to get -5 showing that b works
Gwen is a makeup artist and carries a lot of makeup around with her. She has 8 cosmetics in her bag, including 2 lip glosses.
What is the probability that a randomly selected makeup item from her bag will be a lip gloss?
!!!Write your answer as a fraction or whole number!!!
Answer:
2% hope it helpssss
Step-by-step explanation:
Answer:
2/8 or 1/4
Step-by-step explanation:
So pretty much you just turn the number into a fraction
so 5(4d+8) = 40 so what does d= ?
Answer:
d = 0.
Step-by-step explanation:
First, use the distributive property and distribute the 5.
The equation is now 20d + 40 = 40.
Subtract 40 from both sides to isolate the variable.
The equation is now 20d = 0.
Now you're thinking, this can't be possible! But really, 0 / 20 is possible. The answer is d = 0.
Scott has a container of ping pong balls and golf balls. The number of ping pong balls in the container is 8 times as many as the number of golf balls in the container. If there are 10 golf balls in the container, how many ping pong balls are in the container?
a.88
b.80
c.2
d.18
Answer:
b)
Step-by-step explanation:
Number of ping pong balls = 8 * number of golf balls
= 8*10
= 80
Arrange the numbers 2,3,4,5,6,7,8,9 and 10 in the accompanying triangle so that each side sums to 21 show your answer and please help
All three sides will be equal to 21.
So that is
3 + 7 + 9 + 2 = 21,
3 + 8 + 6 + 4 = 21 and
2 + 10 + 5 + 4 = 21
What are Arithmetic operations?Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Given
Put the Number from 2 to 10 in the circle so that the sum of the Number on each side of a triangle is the same.
3
7 8
9 6
2 10 5 4
So the numbers form a triangle and assume that a circle is drawn on the numbers.
If we add the numbers all the three sides will be equal to 21.
So that is
3 + 7 + 9 + 2 = 21,
3 + 8 + 6 + 4 = 21 and
2 + 10 + 5 + 4 = 21
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What is the area of triangle IHC?
Answer:
[tex]28 cm^2[/tex]
Step-by-step explanation:
The formula for finding the area of a triangle is:
[tex]\frac{1}{2} bh[/tex]
The "b," is the base (7), and the "h," is the height (8):
[tex]\frac{1}{2} (7)(8)[/tex]
[tex]\frac{1}{2} (56)[/tex]
28
"The area of triangle [tex]IHC is $\boxed{\frac{1}{2} \times b \times h}$[/tex], where [tex]$b$[/tex] is the base of the triangle and[tex]$h$[/tex]is the height of the triangle.
To determine the area of triangle IHC, we need to know the lengths of the base and the height. The area of a triangle is given by the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
In the case of triangle IHC, if we let b represent the length of the base IH, and h represent the length of the height from point H to side IH, then the area of triangle IHC can be calculated using these values.
Without specific numerical values for b and h, we cannot calculate a numerical area. However, if the values of b and h are provided, we can substitute them into the formula to find the area. For example, if b = 6 units and h = 4 units, then the area would be:
[tex]\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \][/tex]
Thus, the area of triangle IHC with a base of 6 units and a height of 4 units would be 12 square units. If the actual lengths of the base and height are different, those values should be substituted into the formula to calculate the correct area."
Can someone answers this please
Answer:
y = - 24
Step-by-step explanation:
[tex]y = (x - 4)(x + 6) \\ plug \: x = 0 \\ y = (0 - 4)(0 + 6) \\ y = ( - 4)(6) \\ y = - 24 \\ \purple{ \bold{ \therefore \: y - intercept = - 24}}[/tex]
Georgia participated in a sleep study in which scientists found that she fell into REM sleep exactly every 45 minutes while she
was asleep. If Georgia was asleep for 6 hours (390 minutes), how many periods of REM sleep did she have?
The number of periods of REM sleep Georgia has in the 6 hours (390 minutes) as stated in the question is 8.667 periods.
Using the standard time conversion, the number of periods is 8 hours.
How do we determine the number of periods Georgia falls into in REM sleep using word problems.To determine the number of periods of REM sleep that Georgia has, we need to divide the total number of minutes of sleep by the interval at which she falls into the REM sleep.
From the given information:
Georgia was asleep for = 390 minutesNumber of intervals she falls into REM = every 45 minutesThe number of periods of REM sleep she has in 390 minutes of sleep is:
= 390 minutes/ 45 minutes
= 8.667 periods.
NOTE: We have only 360 minutes in 6 hours since 60 minutes = 1 hour.
= 360 minutes/ 45 minutes = 8 periods.
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If a figure has 90° rotational symmetry, what other symmetries must it have?
Answer:
Step-by-step explanation:
The figure must also have the rotational symmetry of 180/270°.
What are symmetries in math?
In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
What are the four types of symmetries?Types of symmetries are rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry. These four types of symmetries are examples of different types of symmetry on a flat surface called planar symmetry.
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What is the discriminant of the quadratic equation 9x2 – X – 8=0?
Answer:
288
Step-by-step explanation:
a = 9
b = -1
c = -8
b^2 * -4 * ( a * c )
Just filing in the numbers given above:
-1^2 * -4 * ( 9 * -8 )
1 * -4 * ( -72)
1 * + 288 = 288
which measurement is equal to 6 kilograms?
6,000 grams
600 milligrams 600 grams
600milligrams
HURRY PLZ HELP I WILL GIVE BRAINLY
The measurement which is equal to 6 kilograms is; 6,000 grams.
In measurements, ground units are sometimes supported with prefixes to express fractions or multiples of the ground units.
On this note, the ground unit grams when supported by kilo- means; 1000 grams.
Ultimately, the measurement which is equal to 6 kilograms is 6,000 grams.
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A small bar of gold measures 40mm by 25mm by 2mm. One cubic millimeter of gold weighs about 0.0005 ounce. Find the voulme in cubic millimeters and the weight ounces of the small bar of gold.
Answer:
Look below for answer!
Step-by-step explanation:
Hope this Helps!!!
⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇
Which best describes the range of the function f(x)=2(1/4)x after it has been reflected over the y-axis
Answer: all real numbers greater than zero
Step-by-step explanation: If you graph this function then you realize that the line does not ever reach 0 on the y axis but instead 'evens out' which means that any number greater than 0 will be the range of the above stated function
Answer: C. All real numbers greater than zero
Step-by-step explanation:
You use the associative property of multiplication to change how factors
are grouped. In the example, why are the factors of the term 3 x 7a
regrouped as (3 x 7)a?
Your answer
Answer:3x7
Step-by-step explanation:
Okay so I don’t think I can get it to you tomorrow or tomorrow if you want to know if you want
the factors of the term [tex]3 \times (7a)[/tex] are regrouped as [tex](3 \times 7) \times a[/tex] so that by using the associative property we can simplify the multiplication process and ensure consistency in mathematical calculations.
The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product. This property can be written mathematically as:
[tex](a \times b) \times c = a \times (b \times c)[/tex].
In the example, the factors 3 and 7a are initially grouped as [tex]3 \times (7a)[/tex]. Using the associative property, we regroup them as [tex](3 \times 7) \times a[/tex]. This shows that it doesn't matter how we group the numbers; the product will be the same.
For instance:
[tex]3 \times 7a = (3 \times 7) \times a = 21a[/tex]
This regrouping can make calculations simpler because it allows us to first multiply 3 and 7 to get 21 and then multiply by the variable a, rather than working directly with the expression 7a.
In the example, the factors of the term [tex]3 \times (7a)[/tex] are regrouped as [tex](3 \times 7) \times a[/tex] so that by using the associative property we can simplify the multiplication process and ensure consistency in mathematical calculations.
Which function, gor h, is the inverse function for function f?
A. the function gbecause the graphs of fand gare
symmetrical about the line y= x
CB. the function g because the graphs of fand gare
symmetrical about the x-axis
C. the function h because the graphs of fand hare
symmetrical about the line y= x
D. the function h because the graphs of fand hare
symmetrical about the x-axis
evaluate the expression for q=8
7q
Answer:
The answer is 56.
Step-by-step explanation:
7 * 8 = 56
Tickets to a circus cost $38.50 each. the glee club bought 70 tickets for saturdays circus and 21 tickets for sunday's circus. how much did the glee club pay in all for the tickets's?
Answer:
$878.5
Step-by-step explanation:
that is if the tickets for saturday & sunday are both $38.50
Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the
ground 9 feet away. A bug crawled from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake. How
far did the bug crawl?
feet
The bug crawl in total of 90 feet of distance .
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
According to question
Ataut telephone wire extends from the top of a 40-foot tall telephone pole to a stake in the ground 9 feet away
So, according to diagram
AB= 9 feet
AC = 40 feet
BC =[tex]\sqrt{AB^{2} +AC^{2} }[/tex](Pythagoras theorem)
BC = [tex]\sqrt{9^{2} +40^{2} }[/tex]
BC=[tex]\sqrt{81 + 1600 }[/tex]
BC = [tex]\sqrt{ 1681 }[/tex]
BC= 41 feet
As bug start from the stake in the ground up the wire to the top of the
telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake which means perimeter of right angle triangle.
Perimeter of triangle = AB + BC + AC
= 9 + 41 + 40
= 90 feet
Hence, the total distance travelled by bug is 90 feet .
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Jared is at the grocery store buying dog food for his dogs. He wants to purchase the dog food at the lowest price per ounce. The table below shows the number of pounds of the different bags of food and the prices.
Bag Size
(in pounds)
Price
5 $4.80
10 $7.90
20 $16.20
50 $40.00
Which size bag of dog food should Jared buy?
Jared should buy the 10-pound bag of dog food to get the lowest price per ounce.
To determine which size bag of dog food Jared should buy to get the lowest price per ounce, we need to calculate the price per ounce for each bag size and then compare them.
First, we convert the weight of each bag from pounds to ounces, knowing that 1 pound equals 16 ounces. Then we calculate the price per ounce by dividing the price of each bag by the number of ounces it contains.
Here are the calculations:
1. For the 5-pound bag:
- 5 pounds * 16 ounces/pound = 80 ounces
- Price per ounce = $4.80 / 80 ounces = $0.06 per ounce
2. For the 10-pound bag:
- 10 pounds * 16 ounces/pound = 160 ounces
- Price per ounce = $7.90 / 160 ounces = $0.049375 per ounce
3. For the 20-pound bag:
- 20 pounds * 16 ounces/pound = 320 ounces
- Price per ounce = $16.20 / 320 ounces = $0.050625 per ounce
4. For the 50-pound bag:
- 50 pounds * 16 ounces/pound = 800 ounces
- Price per ounce = $40.00 / 800 ounces = $0.05 per ounce
Now, comparing the price per ounce for each bag, we find that the 10-pound bag offers the lowest price per ounce at $0.049375.
Therefore, Jared should buy the 10-pound bag of dog food to get the lowest price per ounce.
The correct answer is the 10-pound bag of dog food.
a penny is dropped from the top of the building and takes 9 seconds to fall to the ground. What is the height of the building D=distance T=Time
The height of the building is 9x.
What is Distance- time formula?Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time.
Given:
Time= 9s
Let the speed of penny be 'x'.
We know,
speed = distance / time
distance = speed* time
distance = x *9
distance = 9x.
Learn more about this Distance- time formula here:
https://brainly.com/question/13704700
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The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number?
Answer:
0.06 or 6%
Step-by-step explanation:
Both bags have the numbers 5, 6, 7, 8, 9 and 10. Thus, there are 6 similar number in both bags.
The probability of picking the number 5 in both bags is:
P(5)= 1/10 * 1/10= 1/ 100
It is the same probability of picking the number 6 or 7 or 8 or 9 or 10 in both bags.
P ( 6)= 1/100
P ( 7 ) = 1 /100
P (8)= 1 /100
P ( 9 ) = 1 /100
P ( 10 ) = 1 /100